scipy.special.eval_sh_chebyt

scipy.special.eval_sh_chebyt(n, x, out=None) = <ufunc 'eval_sh_chebyt'>

Evaluate shifted Chebyshev polynomial of the first kind at a point.

These polynomials are defined as

\[T_n^*(x) = T_n(2x - 1)\]

where \(T_n\) is a Chebyshev polynomial of the first kind. See 22.5.14 in [AS] for details.

Parameters

narray_like

Degree of the polynomial. If not an integer, the result is determined via the relation to eval_chebyt.

xarray_like

Points at which to evaluate the shifted Chebyshev polynomial

outndarray, optional

Optional output array for the function values

Returns

Tscalar or ndarray

Values of the shifted Chebyshev polynomial

See also

roots_sh_chebyt

roots and quadrature weights of shifted Chebyshev polynomials of the first kind

sh_chebyt

shifted Chebyshev polynomial object

eval_chebyt

evaluate Chebyshev polynomials of the first kind

numpy.polynomial.chebyshev.Chebyshev

Chebyshev series

References

AS

Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.